A universal joint (U-joint) is a type of coupling that can be attached to a shaft to allow the shaft to rotate and transmit rotational motion in other than a straight line, such as by coupling together multiple shaft segments that allows the segments shaft to bend, turn, or accommodated non linear paths while transmitting torque, rotary motion, or both between the shaft segments and opposing ends of the shaft. Rotating shafts or elements transmitting torque are present in many applications, and are also in use in vehicles, such a automobiles, trucks, tractors, machinery, and equipment. For example, on vehicles where the engine is located on a different end from the drive wheels, such as on rear-wheel drive trucks, and on many 4-wheel drive vehicles, a driveshaft is used transfer torque from the engine and transmission to the drive wheels. To permit variations in alignment, a driveshaft typically incorporates several universal joints (U-joints).
FIG. 1 illustrates the concept of operating angles of a shaft having multiple U-joints. As shown in FIG. 1, a first shaft segment 1 is coupled to a second shaft segment 2 using a first U-joint A, and the second shaft segment 2 is coupled to a third shaft segment 3 using a second U-joint B. As illustrated, each shaft segment is coupled to another at an angle, called the operating angle. For instance, the operating angle between the first shaft segment 1 and the second shaft segment 2 is a degrees (a°) and the operating angle between the first shaft segment 2 and the third shaft segment 3 is b degrees (b°). It is known in the art that when U-joints are used to accommodate operating angles a° and b° and the operating angles a° and b° are the same, the rotational speed of the first shaft segment 1 and the third shaft segment 3 will also be the same. Additionally, when the operating angles a° and b° are the same and the first shaft segment 1 is rotated at a constant rate, the third shaft segment 3 will also rotate at a constant rate.